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Chapter 20: Problem 87

A uranium- 235 nucleus decays by a series of alpha and beta emissions until it reaches lead-207. How many alpha emissions and how many beta emissions occur in this series of decavs?

Short Answer

Expert verified
7 alpha and 4 beta emissions occur.

Step by step solution

01

Understanding Alpha and Beta Emissions

Alpha emission reduces the mass number by 4 and the atomic number by 2 (the nucleus loses 2 protons and 2 neutrons). Beta emission increases the atomic number by 1 (a neutron is converted into a proton). We need to account for the changes in both the mass and atomic numbers to determine the number of emissions.
02

Calculating Change in Mass Number

The mass number of uranium-235 is 235, and it decays to lead-207. The mass number change is \(235 - 207 = 28\). Since each alpha emission reduces the mass number by 4, the number of alpha emissions is \(\frac{28}{4} = 7\).
03

Calculating Change in Atomic Number

The atomic number of uranium (U) is 92, and the atomic number of lead (Pb) is 82. The total change in atomic number is \(92 - 82 = 10\). Each alpha decay reduces the atomic number by 2, so from 7 alpha emissions, we have a reduction of \(7 \times 2 = 14\). To explain the remaining 4 increase, 4 beta emissions are necessary since each beta decay increases the atomic number by 1.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Alpha Decay
Alpha decay is a type of radioactive decay where an unstable nucleus emits an alpha particle. An alpha particle consists of two protons and two neutrons; essentially, it's identical to a helium nucleus. When a nucleus undergoes alpha decay, it loses the alpha particle, which results in two important changes to the nucleus:
  • The mass number decreases by 4.
  • The atomic number decreases by 2.
This process is common in heavy elements such as uranium and thorium that have large atomic numbers. The loss of mass and charge helps stabilize these nuclei. Alpha particles themselves are not very penetrating and can be stopped by a piece of paper or skin.
Beta Decay
Beta decay is another mode of radioactive decay, distinguished by its conversion of a neutron into a proton within the nucleus, emitting an electron (known as a beta particle) and an antineutrino. During beta decay:
  • The mass number remains unchanged.
  • The atomic number increases by 1.
This occurs because a neutron is transformed into a proton, which stays in the nucleus, while the emitted beta particle is expelled. Beta decay allows the atom to move closer to a stable state by rearranging the proportions of protons and neutrons. Unlike alpha particles, beta particles can penetrate materials more deeply, requiring materials like plastic or glass to block them.
Uranium-235
Uranium-235 is a naturally occurring isotope of uranium, notable for its ability to undergo nuclear fission as well as radioactive decay. With a mass number of 235 and an atomic number of 92, uranium-235 is unique because:
  • It's one of the few fissile materials suitable for nuclear reactors and weaponry.
  • It decays into various products, eventually stabilizing as lead-207 through a decay chain of successive alpha and beta emissions.
The fission properties of uranium-235 make it crucial in energy generation. Its decay process involves a series of changes that affect both the mass and atomic numbers, which are essential in calculating emissions during its transition to lead.
Lead-207
Lead-207 is the stable end product of the uranium-235 decay chain. This stable isotope has a mass number of 207, and it is the safe, non-radioactive conclusion to numerous decay processes. Through this lengthy decay sequence:
  • Uranium-235 sheds part of its mass through alpha emissions.
  • Its atomic structure rearranges through beta emissions until it reaches lead-207.
Lead-207 does not undergo further radioactive decay and is an example of how unstable, radioactive nuclei can eventually become stable. Understanding the transformation from uranium-235 to lead-207 not only provides insight into nuclear physics but also into issues related to radiological safety and the dating of geological formations.

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Most popular questions from this chapter

What is a radioactive tracer? Give an example of the use of such a tracer in chemistry.

A sample of sodium- 24 was administered to a patient to test for faulty blood circulation by comparing the radioactivity reaching various parts of the body. What fraction of the sodium- 24 nuclei would remain undecayed after \(12.0 \mathrm{~h} ?\) The half-life is \(15.0 \mathrm{~h}\). If a sample contains \(6.0 \mu \mathrm{g}\) of \({ }^{24} \mathrm{Na}\), how many micrograms remain after \(12.0 \mathrm{~h}\) ?

Thorium is a naturally occurring radioactive element. Thorium-232 decays by emitting a single alpha particle to produce radium-228. Write the nuclear equation for this decay of thorium-232.

A bismuth-209 nucleus reacts with an alpha particle to produce an astatine nucleus and two neutrons. Write the complete nuclear equation for this reaction.

Some mammoth bones found in Arizona were found by carbon- 14 dating to be \(1.13 \times 10^{4}\) years old. What must have been the activity of the carbon-14 in the bones in disintegrations per minute per gram? Assume the original activity was 15.3 disintegrations per minute per gram.
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